CLINICAL KIDNEY JOURNAL
Clinical Kidney Journal, 2016, vol. 9, no. 4, 527–529
doi: 10.1093/ckj/sfw050
Advance Access Publication Date: 19 June 2016
Editorial Comment
EDITORIAL COMMENT
Formulas for fixing serum sodium: curb your enthusiasm
Richard H. Sterns
University of Rochester School of Medicine and Dentistry, Rochester General Hospital, 1425 Portland Avenue,
Rochester, NY 14534, USA
Correspondence and offprint requests to: Richard H. Sterns; E-mail: [email protected]
Abstract
A variety of formulas have been proposed to predict changes in serum sodium concentration. All are based on an experiment
done over 50 years ago by Edelman, who derived a formula relating the plasma sodium concentration to isotopically measured
body sodium, potassium, and water. Some of these formulas fail because they do not include urinary losses of electrolytes and
water. Even those that include these essential variables are not accurate enough for clinical use because it is impractical to
adjust calculations to rapid changes in urinary composition, and because the formulas do not account for changes in serum
sodium caused by internal exchanges between soluble and bound sodium stores or shifts of water into or out of cells resulting
from changes in intracellular organic osmolytes. Nephrologists should curb their enthusiasm for predictive formulas and rely
instead on frequent measurements of the serum sodium when correcting hyponatremia and hypernatremia.
Key words: hyponatremia, hypernatremia, hypertonic saline, organic osmolytes
Nephrologists love formulas. It is fun to mathematically predict
what nature is about to do or to explain what it has already
done. Formulas elevate us above our colleagues and our students,
who gaze in awe as we take to the blackboard to explain acid–base
and fluid electrolyte problems that often leave them baffled.
However, it is important that we do not get too carried away
with our mathematical friends. Most formulas we use are estimates based on clinical reasoning, limited clinical data or biochemical measurements of uncertain validity. The fractional
excretion of sodium (FENa) gives us an estimate of fractional sodium excretion, but it is based on the serum and urine creatinine
concentrations, which provide an imperfect estimate of glomerular filtration; its predictive value for distinguishing prerenal azotemia from other causes of kidney injury is based on very limited
data. A correction factor that we used for years to correct the
serum sodium for the osmotic water shift caused by hyperglycemia was based on armchair reasoning [1]; another estimate,
which many of us adopted in its place, was based on a single
small experiment that raised blood glucose in volunteers with
somatostatin infused with 5% dextrose in water [2]. The transtubular potassium gradient (TTKG), which we have used to define
potassium secretion in the aldosterone-sensitive distal nephron,
is based on clinical reasoning augmented by laboratory experiments that proved to be flawed; its creators recommend that it
not be used, but many nephrologists still cling to it [3, 4].
In this issue of Clinical Kidney Journal, Hahna et al. [5] assess the
accuracy of four equations that have been proposed to predict the
response of the serum sodium concentration to intravenous
fluids containing various concentrations of sodium and potassium; none of the forecasts were precise enough to guide therapy.
All of these formulas are based on an experiment done >50 years
ago by Edelman et al. [6], who identified a group of patients with
widely varying serum sodium concentrations; measured exchangeable sodium, exchangeable potassium and total body
water using isotopes; and then, using linear regression, derived
a formula relating the sodium concentration in plasma water to
these variables. The equation that emerged had a y-intercept,
i.e. the regression line did not pass through zero as would be
Received: May 10, 2016. Accepted: May 11, 2016
© The Author 2016. Published by Oxford University Press on behalf of ERA-EDTA.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/
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| R.H. Sterns
expected if sodium and potassium were simply solutes dissolved
in a volume of water [7]. In fact, a substantial fraction of the sodium measured isotopically is not free in solution, but is actually
bound to large macromolecules called proteoglycans, in skin,
cartilage and bone [8].
There are several reasons why formulas may fail to accurately
predict the response of serum sodium concentration to our therapies. The serum sodium concentration is determined by the
amount of sodium and potassium dissolved in body fluids, and
by the volume of body water:
Serum ½Na ¼
Total body soluble ðNa þ K)
:
Total body water
Many clinicians and some formulas focus solely on the effect of
intravenous fluids on this relationship: a solution whose concentration of (Na + K) is higher than that of plasma is expected to
raise the serum sodium concentration, while a solution with a
lower (Na + K) concentration is expected to lower it; the magnitude of the response is calculated with an algebraic reformulation of the Edelman et al. relationship that adds the intravenous
solution’s electrolyte content to the numerator and its volume to
the denominator of the equation [9].
Predictive formulas that ignore urinary electrolyte and water
losses are doomed to failure. It should be obvious that net balances of sodium, potassium and water (input − output) must be
considered [10]. Urinary electrolyte and water losses often have a
greater impact on the serum sodium concentration than do intravenous fluids [8]. The serum sodium concentration of a hypernatremic patient with complete diabetes insipidus who excretes
12 L of dilute urine daily (500 mL/h) will continue to rise during
the infusion of 5% dextrose in water at 250 mL/h; formulas
based only on fluid intake will erroneously predict correction of
hypernatremia by 1 mEq/L/h.
Some formulas take urine losses into account, requiring measurements of urine sodium and potassium concentrations and
urine volume. However, such measurements are single frames
of what is often a complex movie; when treating hyponatremia,
urine composition may change abruptly during the course of
therapy. For example, consider a patient with hyponatremia
caused by iatrogenic syndrome of inappropriate antidiuretic hormone secretion (SIADH) due to desmopressin. The urine electrolyte concentration may be higher than plasma at presentation,
but if desmopressin is discontinued, the urine will become dilute
once the antidiuretic effect of the drug has abated; urine electrolyte concentrations will then rapidly fall while urine volume increases, and the serum sodium concentration will increase far
more rapidly than the formula predicts.
Conversely, if saline solutions are given to patients with persistent SIADH, volume expansion will eventually provoke a natriuresis,
and, if the urine osmolality is higher than plasma osmolality, excretion of salt in a hypertonic urine can actually cause the serum sodium to fall, the opposite of the formula-predicted response [11, 12].
An unanticipated water diuresis is quite common during the
course of therapy of severe hyponatremia and often leads to inadvertent overcorrection. In one retrospective series of patients
with serum sodium concentrations <120 mEq/L who were treated
with 3% saline, the increase in serum sodium exceeded the increase predicted by the original Adrogue–Madias equation
(based solely on the initial serum sodium and the composition
of intravenous fluids) in 74.2% of patients; the average correction
in overcorrectors was 2.4 times the predicted. Inadvertent overcorrection was due to documented water diuresis in 40% of patients [13]. The cause of water retention in most patients with
severe hyponatremia is reversible. As soon of the cause of
water retention (hypovolemia, thiazide diuretics, antidepressants, desmopressin, cortisol deficiency or transient SIADH due
to pain, stress or nausea) is eliminated, antidiuretic hormone levels become maximally suppressed, and the ensuing water diuresis may increase the serum sodium concentration over 2 mEq/L/
h, equivalent to the effect of infusing 3% saline at 150 mL/h. To
avoid overcorrection, the clinician must either match urine
water losses with 5% dextrose in water, or stop the losses by administering desmopressin [14, 15]. Alternatively, such a water diuresis can be anticipated, and treated proactively with
desmopressin at the outset of therapy, creating a state of iatrogenic SIADH, in which urinary water losses are eliminated as a
variable; the serum sodium concentration is then increased
with the concurrent infusion of 3% saline [15–17]. With the concurrent administration of desmopressin and 3% saline, the increase in serum sodium concentration is more predictable, but
the actual increase in serum sodium concentration may still deviate from what formulas project.
The Nguyen–Katz equation is the most rigorous predictive formula, because unlike others, it includes the pesky y-intercept
found in Edelman et al. original linear regression [18]. As
mentioned earlier, the intercept likely has biological meaning; it reflects the insoluble sodium bound to anionic sites on proteoglycans
in skin, cartilage and bone. Inaccurate predictions will still occur
with this equation if urinary composition changes during the
course of therapy. However, even if the electrolyte concentrations
and volume of all intake and output could be measured continuously, and changes in composition captured and counted, it is
still possible that the actual sodium might deviate from the concentration predicted by the equation. The Nguyen–Katz equation
assumes that the intercept in Edelman et al. equation is constant.
In fact, there is evidence that sodium bound to proteoglycans can
serve as a reservoir that can either absorb excess sodium from
the soluble pool or contribute to it when sodium is in short supply;
such exchanges between soluble and bound sodium pools would
make the intercept a variable rather than a constant.
Most predictive equations assume that electrolytes are the
only solutes that alter the serum sodium concentration. This is
not always true. Clinicians are familiar with the effect of hyperglycemia and exogenous solutes like mannitol on the serum sodium concentration. Intracellular organic osmolytes may also
affect the serum sodium concentration. These solutes play an
important role in the adaptation of the brain to hyponatremia
and hypernatremia; depletion of brain cell osmolytes in hyponatremia and accumulation of extra osmolytes in hypernatremia
minimize the change in cell volume that occurs in these disturbances [8]. Organic osmolytes are also present in other cells
and could potentially alter the relationship between body electrolytes and serum sodium concentration [19]. For example, depletion of intracellular organic osmolytes in response to
chronic hyponatremia would result in a shift of intracellular
water to the extracellular fluid, minimizing cell swelling, but lowering the serum sodium concentration. Repletion of cell osmolytes during correction of hyponatremia would result in a shift
of water back to the cells, and a greater increase in serum sodium
concentration than would be predicted by any formula based on
the Edelman et al. equation. Such a phenomenon was suspected
in a series of severely hyponatremic patients treated with 3% saline and desmopressin [17]. One would expect that with time, because of volume expansion, urinary losses of sodium would
accelerate during administration of hypertonic saline, blunting
the effect of the intravenous fluid on the serum sodium concentration. In fact, the opposite occurred; the increase in serum
CLINICAL KIDNEY JOURNAL
Editorial Comment
sodium in response to hypertonic saline was greater on the second day of the protocol, as might occur with time-dependent repletion of lost intracellular organic osmolytes.
Minor differences between actual and predicted changes in the
serum sodium concentration are more important now than they
had been in the past. It was once fashionable to ‘half-correct’ the
serum sodium concentration within a few hours. It is now known
that in patients with severe hyponatremia, this practice often
leads to osmotic demyelination syndrome [20, 21]. Most authorities now recommend correction rates of 4–6 mEq/L/day to avoid
this complication [22, 23]. With goals this small, a 1–2 mEq/L
deviation from predicted increases can no longer be tolerated.
Nephrologists should curb their enthusiasm for predictive formulas and rely instead on a strategy that may be less intellectually
satisfying, but ultimately more successful: when fixing the
serum sodium concentration, measure the serum sodium concentration and measure it often.
8.
9.
10.
11.
12.
13.
14.
(See related article by Hanna et al. The utility and accuracy of four
equations in predicting sodium levels in dysnatremic patients.
Clin Kidney J (2016) 9: 530–539.)
15.
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